In this article, the analysis and design problems of H_∞ filtering for a class of discrete‐time switched singular systems with time‐varying delay under an arbitrary switching signal are investigated. The main attention is focused on the design of a linear mode‐dependent filter guaranteeing the regularity, causality, and asymptotic stability of the resulting filtering error system with a prescribed H_∞ performance bound. By using a multiple Lyapunov‐Krasovskii functional, and utilizing the linearization technique, novel sufficient conditions for the solvability of H_∞ problem are derived in terms of linear matrix inequalities. Solving that, the desired filter gains can be determined. Any model transformation of system, which often leads the large computational burden is involved. The free weighting matrix technique is introduced to provide additional degree of freedom, which improves the conservativeness of the developed method. Finally, numerical examples are given to demonstrate the effectiveness and the merit of the proposed approach and to compare the obtained results with some previous works in the literature.

中文翻译：

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具有时变时滞的离散时间奇异系统的H∞滤波

本文研究了在任意切换信号下一类具有时变时滞的离散时间切换奇异系统的_H∞滤波分析和设计问题。主要关注点集中在线性模式相关滤波器的设计上，该滤波器可确保所产生的滤波误差系统具有规定的_H∞性能界限，从而具有规律性，因果关系和渐近稳定性。通过使用多个Lyapunov-Krasovskii泛函，并利用线性化技术，为_H∞的可溶性提供了新颖的充分条件问题是根据线性矩阵不等式得出的。解决该问题，可以确定所需的滤波器增益。涉及系统的任何模型转换，这通常会导致较大的计算负担。引入了自由加权矩阵技术以提供额外的自由度，从而提高了所开发方法的保守性。最后，通过数值算例说明了该方法的有效性和优点，并将所得结果与文献中的某些先前工作进行了比较。